Warm-up

Agenda Learn about famous books Begin Chapter 1 Review Coordinate Plane Discover Basic Building Blocks Points, Lines, & Planes Bring book tomorrow (Thursday)

Books… The Elements Euclid 300 BC Required reading for 2000 years Over 1000 editions Most popular textbook

More books… Flatland Flatterland Edwin Abbott Abbott 1884 novella Satire on Victorian Society Primer for school geometry Flatterland Ian Stewart 2001 Flatland – 0 to 3 dimensions – Euclidean Geometry Edwin A Abbott – Headmaster 1884 Flatterland – Euclidean & Non-Euclidean, Physics Ian Stewart 2001

1-1 Coordinate Plane II I IV III Quadrants y-axis Ordered Pair (x-coordinate, y-coordinate) (2, 3) II I y-axis Chapter 1 Section 1-1 Coordinate Plane (What is missing? Arrows) x-axis, y-axis, Origin Point - (1,2) - (x coordinate, y coordinate) - Ordered Pair Two Points (1,2) (4,4) - Line Quadrants I (+,+) II (-,+) III (-,-) IV (+,-) What popular kid’s game uses two coordinate planes? (Battleship) x-axis IV III

Determine Coordinates Point Quadrant O ( 0 , 0 ) Origin P ( 2 , -5 ) IV Q ( -3 , -4 ) III R ( 0 , -2 ) y-axis O Plot points and have students determine their coordinates. O (0,0) Origin P (2, -5) IV Q (-3,-4) III R (0,-2) y-axis R Q P

What do you see? X Y A B C (0,4) -4 -2 -8/3 4 2 7 (-8/3, 0) 4 2 7 (-8/3, 0) What can you tell me about these three objects? All represent the same set of data points.

Collinear/Noncollinear Plot three points, connect Add fourth point, not on line Draw second line connecting fourth point to one point on line, now they are collinear B D A

Answers Ahead

Study Guide 1-1

Section 1-2 Points P Basic building block Zero dimension (no size) Named with a capital letter Draw point A Draw point B Flatland – lonely, isolated objects P

Lines m Continuous set of points One dimension (length) Named with a lower case script letter or by two points on the line Draw points A and B, make line AB (remember arrows), name it lower case script m (arrows indicate line extends indefinitely) Show possible names line AB, line BA, AB (under arrow), BA (under arrow) Draw line with points R, S, T, U (Flatland – points only know neighbor) 12 possible names RS, RT, RU, ST, SU, TU, UT, US, UR, TS, TR, SR (under arrows) Why doesn’t it matter what you name it? Line segment – distance from one point to another Named with two points under a straight line B m A

Plane Continuous points, multiple lines Two dimensions (length, width) Named with a capital (uppercase) script letter S Draw plane with noncollinear points P, Q, S – name it R Points are coplaner, some points with also be collinear Much richer environment, many 2D shapes P R Q

Point, Line, Plane Undefined terms in Geometry Can use examples and descriptions to define but not rigorous mathematics Terms are used to define more complex geometric terms, shapes and properties

Some basic rules A point can be on multiple lines and planes P l m

Intersecting lines Two lines intersect at one point, no points or all points p The intersection of two figures is the set of points that are contained in both figures. Both lines contain point T. Draw Point A, show multiple lines, plane Show following slide Add parallel line Add coincident line Show third slide n

Lines and Planes A line can intersect a plane or be contained within a plane A line intersects a plane at a single point Point R on line m and plane N. All of l is contained by plane N

Intersecting Planes Two planes intersect at a line Line AB is on planes P and Q.

Points, lines & planes Line AB is on planes P and Q.

Points, lines & planes Line AB is on planes P and Q.

Points, lines & planes Line AB is on planes P and Q.

Points, lines & planes Line AB is on planes P and Q.

Points, lines & planes Line AB is on planes P and Q.

Answers Ahead

Study Guide 1-2

Study Guide 1-2

Homework Define point, line and plane in your own words. Finish Study Guides, Practice pages Section 1-1 Section 1-2